On a class of polynomial differential systems of degree 4 : Phase portraits and limit cycles
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Salhi, Tayeb (Université de Bordj Bou Arréridj. Département de Mathématiques (Algeria))

Date:	2021
Abstract:	In this paper we characterize the phase portraits in the Poincaré disc of the class of polynomial differential systems of the form ẋ = −y, ẏ = x + ax4 + bx2 y2 + cy4, with a2 + b2 + c2 ≠ 0, which are symmetric with respect to the x-axis. Such systems have a center at the origin of coordinates. Moreover, using the averaging theory of five order, we study the number of limit cycles which can bifurcate from the period annulus of this center when it is perturbed inside the class of all polynomial differential systems of degree 4.
Grants:	Agencia Estatal de Investigación MTM2016-77278-P Ministerio de Economía y Competitividad MDM-2014-0445 Agència de Gestió d'Ajuts Universitaris i de Recerca 2017/SGR-1617 European Commission 777911
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Polynomial differential systems ; Polynomial vector fields ; Phase portraits ; Centers ; Limit cycles
Published in:	Topological Methods in Nonlinear Analysis, Vol. 57, Issue 2 (June 2021) , p. 441-463, ISSN 1230-3429

DOI: 10.12775/TMNA.2020.042

Postprint 21 p, 806.2 KB

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